The invention relates to the field of ribbon beam amplifier, and in particular to a three-dimensional (3D) design of a non-axisymmetric periodic permanent magnet (PPM) focusing field for a ribbon-beam amplifier (RBA).
High-intensity ribbon (thin sheet) beams are of great interest because of their applications in particle accelerators and vacuum electron devices. Recently, an equilibrium beam theory has been developed for an elliptic cross-section space-charge-dominated beam in a non-axisymmetric periodic magnetic focusing field.
In the equilibrium beam theory, a paraxial cold-fluid model is employed to derive generalized envelope equations which determine the equilibrium flow properties of ellipse-shaped beams with negligibly small emittance. The magnetic field is expanded to the lowest order in the direction transverse to beam propagation. A matched envelope solution is obtained numerically from the generalized envelope equations, and the results show that the beam edges in both transverse directions are well confined, and that the angle of the beam ellipse exhibits a periodic small-amplitude twist. Two-dimensional (2D) particle-in-cell (PIC) simulations with a Periodic Focused Beam 2D (PFB2D) code show good agreement with the predictions of equilibrium theory as well as beam stability.